Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–

Abstract

The hierarchy of Kadomtsev-Petvisahvili (KP) equation is studied on the basis of free fermion operators. Particular emphasis is laid on relating the operator approach to the Grassmann formulation of M. and Y. Sato. A new bilinear identity for wave functions is derived, and is shown to generate the series of Hirota bilinear equations for the KP hierarchy. Extension to the multicomponent case is also discussed.